Y. Zarmi

Design and optimization of solar industrial hot water systems with storage

Abstract This paper presents a new method for the design and optimization of solar industrial process hot water systems with storage. The single-pass open-loop design thermally “decouples” collectors from storage, hence insuring that collectors always heat the coldest fluid possible and that stored heat can be completely depleted by the nighttime load. So the single-pass open-loop design, in spite of the relatively low flow rates entailed, operates at higher system efficiency than conventional system designs. One solved example for an an industrial hot water application shows that the single-pass open-loop design delivers about 30 per cent more useful energy with roughly 30 per cent less storage than the conventional design. Moreover, storage tanks do not have to stand high pressures and can thus be significantly cheaper than in conventional systems. The effects of collector operating time, heat exchangers, and secondary system losses are also treated. The new method is extended to cover systems that require weekend storage. The introduction of weekend storage may be cost effective because it enables the designer to reduce collector area without reducing the yearly useful energy delivered by the system.

A typical meteorological day (TMD) approach for predicting the long-term performance of solar energy systems☆

Abstract A method for predicting the long-term performance of solar energy systems, based on the analysis of system performance for one particular day—the typical meteorological day (TMD)—is presented. The TMD is constructed from the cumulative time distribution of insolation values on the collector aperture. The TMD method requires little calculational effort and a small data base relative to standard yearly computer simulations. Good agreement is found between the predictions of the new method and the corresponding results of the F -f-chart method. The TMD method is of particular value for cases that may often be treated inaccurately by simple calculational methods: (1) high threshold problems; (2) systems with short response times (e.g., due to small storage); and (3) systems in which collectors other than flat plates are used (the method is applicable to all solar collector types).

The utilizability function—I Theoretical development of a new approach

Abstract A new theoretical approach to the calculation of the utilizability function is developed and applied to the case of the annual performance of solar collectors of high concentration ratio. The utilizability is calculated in mathematical closed form as an integral over the contributions of the daylight hours of one representative day, equinox. The daily variations in the instantaneous solar radiation (due, for example, to varying degrees of cloudiness) are represented by random fluctuations superimposed on the clear day radiation pattern. The results are in good agreement with the corresponding utilizability curves that are based on detailed meteorological data. A simple and practical analytic expression for the utilizability is derived for the limiting case of clear climates, and turns out to provide rather accurate predictions for the utilizability for all climates as well. The presentation is divided into two separate papers: the current paper, in which the details of the theory and derivation are presented, and the following paper, for the reader who may not not be interested in all the details of the derivation, in which the solved numerical examples and the comparisons with results based on detailed meteorological data are presented.

ANALYTICAL EVALUATION OF DIRECT SOLAR HEATING OF SWIMMING POOLS

Abstract An analytical model for the long term thermal performance of swimming pools is developed and shows that the solution for open pools is applicable to enclosed pools with appropriate modification of parameters. From this solution the seasonal heating load of swimming pools, open or closed, can be calculated analytically.

Analytic model for passively-heated solar houses—1. Theory

Abstract A simple analytic method for the prediction of the long-term thermal performance of passively-heated solar houses is presented. The treatment includes a new coarse method for “energy bookkeeping” and the use of a distribution function which represents the frequency of occurrence of different values of the solar load ratio. Due to its generality, this formalism is applicable to any passive heating element. As specific examples, the cases of direct gain and water wall houses are treated in detail. Relative to the parameterization of computer simulation results, this method offers the user a design tool that can be used to predict, in closed form, the thermal effect on the house of different building and climatic parameters and is not restricted to a “reference” building. Agreement with published numerical simulation results in satisfactory. The presentation is divided into two separate papers: a users guide for the reader who may not be interested in the details of derivation and validation, and the present paper, in which the theory is presented in detail.

An analytic model for the long-term performance of solar thermal systems with well-mixed storage☆

Abstract A simple analytic method is presented for predicting the long-term performance of solar thermal systems with well-mixed storage and loads that do not vary significantly from day to day. Recognizing that most conventionally designed systems have effective relaxation times that are long relative to the time scale of variations in insolation, but short compared to the time scale for day-to-day variations in insolation, we invoke a constant radiation model and solve the problem within that framework. The results of the analytic method are simple closed-form expressions which enable the user to understand clearly the dependence of system performance on the physically important variables. Good agreement is found between the predictions of the analytic method and the corresponding results of the F -f-chart method and computer simulations. The analytic method is furthermore applicable to all collector types and storage fluids and is not restricted to flat plates and hot water storage. The limitations of the analytic method are discussed and found not to introduce a serious restriction for commonly designed conventional systems.

The utilizability function—II Validation of theory against data-based correlations

Abstract The results of a new theoretical approach to the calculation of annual utilizability are illustrated and validated against utilizabilities that are based on detailed meteorological data. The theory is applied to concentrating solar collectors with tracking about two axes, the polar axis, the horizontal east-west axis, and the horizontal north-south axis, for a wide range of clearness index values. A new simple analytic formula for annual utilizability and its accuracy for the case of concentrating collectors are presented. The ultimate power of the theoretical results lies in the fact that with a knowledge of the annual average clearness index only, one can accurately predict utilizability curves for concentrating solar collectors in any climate. This would be particularly valuable for geographical locations and climates which are not covered by existing correlations or for which years of detailed meteorological data do not exist.

Massive storage walls as passive solar heating elements: An analytic model☆

Abstract A recently developed analytic method for the prediction of the long-term thermal performance of passively-heated solar houses is applied to massive storage wall houses. Our method provides closed-form analytic expressions for the same performance variables that have until now been obtained via large-scale computer simulations. Agreement with published numerical simulation results is satisfactory. The adequacy of representing the heat diffusion through a massive storage wall by a one-node model for the calculation of the long-term thermal performance is demonstrated for the range of wall thicknesses of practical interest. The method is not restricted to a “reference” house. Consequently we predict in closed form the effect on the houses solar heating fraction of varying different building and climatic parameters.

The utilizability method with hourly vs daily insolation data

Abstract The significant difference between using hourly vs daily insolation data in the utilizability method is demonstrated for both the specific case of Bet Dagan, Israel and the more general case of utilizability curves that are generated from hourly and daily insolation correlations. For the annual utilizability curves for flat-plate collectors, the curves based on daily insolation data are shown to be significantly different from the corresponding curves based on hourly data, with the differences between the curves increasing with increasing threshold. A simple explanation for this observation is presented and the importance of the need for accurate utilizability curves at high thresholds is discussed.

Analytic model for passively-heated solar houses—II. Users guide☆

Abstract The results of a recently-developed analytic theory for predicting the long-term thermal performance of passively-heated solar houses are cast in a form that is amenable to immediate use by designers. Specific detailed calculations are carried out for direct gain and water wall houses. The simple manner in which the effects of assorted building modifications (glazing area, thermal mass, storage absorbance and night insulation) can be included is illustrated. These calculations require no degree of mathematical sophistication beyond the use of a hand calculator. The methodology illustrated offers the user a flexibility beyond that of the parameterizations of existing computer simulation results in that the user is not limited to a “reference” building, and the method applies equally well to all types of passively-heated solar buildings.